Validating empirically identified risk factors


Fama and French (J Financ, 33, 3–56. 1992); Fama and French (J Financ, 47, 427–465. 1993) provide discipline altering studies which ended the dominance of Capital Asset Pricing Model (CAPM) and supplanted it with the Fama and French three factor model. The CAPM identified the market factor as the only systematic risk factor; the three factor model added size and value as systematic risk factors. The latter study validated the size and value risk factors by showing a correlation between portfolio and factor time-series returns. This model has been widely accepted but has proved “open-ended” as researchers have mimicked this effort to identify a large number of additional factors. Harvey et al. (Rev Financ Stud, 29, 5–68. 2016) note that researchers have empirically identified 316 factors tested as systematic risk factors and argue that the discipline needs to identify the few relevant risk factors. Motivated by this seemingly futile effort to find the correct set of risk factors, we contribute by suggesting necessary conditions to validate empirically identified risk factors. We apply these conditions to the factors of the original Fama-French model. Based on our analysis we argue that neither the size nor value mimicking factors should be considered systematic risk factors.

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  1. 1.

    See for examples Banz (1981), Basu (1983), Reinganum (1981), Rosenberg et al. (1985).

  2. 2.

    We recognize Roll’s (1977) critique that proxies such as the S&P 500 Index are not perfect measures of the market identified in the CAPM.

  3. 3.

    It seems paradoxical to claim a time series relationship in absence of a cross-sectional relationship. If the market factor explains portfolio time series returns, that relationship identified in this explanation is measured by market beta. If portfolio market betas are consistent over time as shown by Fama MacBeth (1973) then a cross-sectional relationship between beta and returns is a mere identity. Indeed, the same assumption of rational pricing within a market that is used to argue that size and value proxy for risk requires the argument that a cross-sectional relationship between beta and returns must exist given a time series relationship between the market factor and portfolio returns.

  4. 4.

    We also conduct regressions for all possible combinations. Because of space and focus considerations we only report results for the simple regressions here. Full results are available from the author.

  5. 5.

    The Barra Model (Barra Risk Factor Analysis) is a multi-factor model created by Barra Inc., which is used to measure the overall risk associated with a security relative to the market. The Barra Model uses a number of key fundamental factors that represent features of an investment. Some of these factors include yield, earnings growth, volatility, liquidity, momentum, price-earnings ratio, size, leverage, and growth.



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Correspondence to George Chang.

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Pettengill, G., Chang, G. Validating empirically identified risk factors. J Econ Finan 43, 162–179 (2019).

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  • Capital Asset Pricing Model
  • Beta
  • Fama-French 3-Factor Model
  • Systematic Risk Factors
  • Risk-adjusted Returns

JEL Classification

  • G11
  • G12